1. Let A € Mmxp and B € Mpxn. Recall that the definition of matrix multiplication gives that the (i, j)-entry of the product AB is P [AB]ij = Σ Aik Bkj. k=1 Use the definition of matrix multiplication to show that (AB)¹ = BT AT.

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
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Chapter3: Matrices
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1. Let A € Mmxp and B € Mpxn. Recall that the definition of matrix multiplication gives that
the (i, j)-entry of the product AB is
P
[AB]ij = Σ AikBkj.
k=1
Use the definition of matrix multiplication to show that (AB)T = BT AT.
Transcribed Image Text:1. Let A € Mmxp and B € Mpxn. Recall that the definition of matrix multiplication gives that the (i, j)-entry of the product AB is P [AB]ij = Σ AikBkj. k=1 Use the definition of matrix multiplication to show that (AB)T = BT AT.
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